Blues had defender Liam Ridgewell controversially dismissed for deliberate handball 10 minutes before the half-time break to spark a madcap and ultimately decisive flurry of activity.
Shola Ameobi converted the resulting penalty to give the Magpies the advantage and when Steven Taylor powered home a second from Joey Barton's corner, the game looked to be over.
However, Lee Bowyer marked his return to Tyneside with a 45th-minute strike, which went in off Fabricio Coloccini's leg, to give Blues some hope but they failed to take anything from the game and so remain three points above the relegation drop zone.
McLeish said: "Taylor probably should have been off the park leading with his elbow on Cameron Jerome's cheekbone earlier in the game.
"We don't want to see that type of thing. Look at my nose and the stitches I have had over the years. That type of challenge is outlawed, but unfortunately the ref didn't see it.
But, anyway, he got away with it and unfortunately for us, the double-whammy, he gets the goal as well."
On the penalty decision, he added: "It hit his arm and he on was on the line. It wasn't going towards the goal, it was going to the side, but Kevin Nolan was probably in a good position to get on the end of it.
"The referee saw the arm going towards the ball and that is a penalty, those are the rules."